Laboratory frame representation of time-dependent gravitational waveforms

Next-generation gravitational wave (GW) experiments will explore higher frequencies where wavelengths become comparable to the dimensions of the detector. In this regime, GWs may be detected not only through mechanical deformations from tidal forces, but also via induced effective currents in electromagnetic background fields. However, the calculation of these signals often requires transforming the GW metric to all orders into the laboratory frame of the detector. Here, we derive a closed-form expression for the metric transformation of general chirplike waveforms expressed in terms of the transverse-traceless GW metric components, their integral, and their derivative. For more complex signals, where analytical integration is impractical, we provide an efficient approximation based on Taylor expansions of the retarded time to coalescence. We find that quasi-Newtonian chirp signals can be accurately transformed using a monochromatic approximation, while also demonstrating that more complex waveforms require the general transformation, which we derive. Thus, the calculated transformations provide essential tools for designing high-frequency GW experiments and analyzing signals from compact object mergers at mega- to gigahertz frequencies.